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Article

Haslinger, Jaroslav ; Janovský, Vladimír ; Kučera, Radek
Path-following the static contact problem with Coulomb friction. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 104-116
MSC: 65N30, 74M10, 74M15, 74S05 | MR 3204435 | Zbl 1340.74071
Keywords:
contact; Coulomb friction; Signorini problem; finite element method; projection; semi-smooth Newton method; path-following algorithm
Summary:
Consider contact problem with Coulomb friction on two planar domains. In order to find non-unique solutions we propose a new path following algorithm: Given a linear loading path we approximate the corresponding solution path. It consists of oriented piecewise linear branches connected by transition points. We developed a) predictor-corrector algorithm to follow oriented linear branches, b) branching and orientation indicators to detect transition points. The techniques incorporate semi-smooth Newton iterations and inactive/active set strategy on the contact zone.
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